Counting Statistics of Non-Markovian Quantum Stochastic Processes

TL;DR

This paper develops a comprehensive method to analyze non-Markovian quantum transport processes, deriving cumulant generating functions and exploring effects of dissipation on current fluctuations in quantum dots.

Contribution

It introduces a general expression for the CGF of non-Markovian quantum processes and links finite-frequency noise to initial correlations, advancing understanding of quantum transport statistics.

Findings

Derived the CGF for non-Markovian quantum transport.

Connected finite-frequency noise to initial system-environment correlations.

Applied method to dissipative double quantum dot, analyzing dissipation effects.

Abstract

We derive a general expression for the cumulant generating function (CGF) of non-Markovian quantum stochastic transport processes. The long-time limit of the CGF is determined by a single dominating pole of the resolvent of the memory kernel from which we extract the zero-frequency cumulants of the current using a recursive scheme. The finite-frequency noise is expressed not only in terms of the resolvent, but also initial system-environment correlations. As an illustrative example we consider electron transport through a dissipative double quantum dot for which we study the effects of dissipation on the zero-frequency cumulants of high orders and the finite-frequency noise.